In order to realize any power from our escape-wheel
tooth, we must provide an impulse face to the pallets
faced at *f e*; and the problem before us is
to delineate these pallets so that the lever will be
propelled through an arc of eight and one-half degrees,
while the escape wheel is moving through an arc of
ten and one-half degrees. We make the arc of
fork action eight and one-half degrees for two reasons—(1)
because most text-books have selected ten degrees of
fork-and-pallet action; (2) because most of the finer
lever escapements of recent construction have a lever
action of less than ten degrees.

LAYING OUT ESCAPE-WHEEL TEETH.

To “lay out” or delineate our escape-wheel
teeth, we continue our drawing shown at Fig. 6, and
reproduce this cut very nearly at Fig. 8. With
our dividers set at five inches, we sweep the short
arc *a a’* from *f* as a center.
It is to be borne in mind that at the point *f*
is located the extreme point of an escape-wheel tooth.
On the arc *a a* we lay off from *p* twenty-four
degrees, and establish the point *b*; at twelve
degrees beyond *b* we establish the point *c*.
From *f* we draw the lines *f b* and *f
c*; these lines establishing the form and thickness
of the tooth *D*. To get the length of the
tooth, we take in our dividers one-half a tooth space,
and on the radial line *p f* establish the point
*d* and draw circle *d’ d’*.

To facilitate the drawing of the other teeth, we draw
the circles *d’ c’*, to which the
lines *f b* and *f c* are tangent, as shown.
We divide the circle *n n*, representing the
periphery of our escape wheel, into fifteen spaces,
to represent teeth, commencing at *f* and continued
as shown at *o o* until the entire wheel is divided.
We only show four teeth complete, but the same methods
as produced these will produce them all. To briefly
recapitulate the instructions for drawing the teeth
for the ratchet-tooth lever escapement: We draw
the face of the teeth at an angle of twenty-four degrees
to a radial line; the back of the tooth at an angle
of thirty-six degrees to the same radial line; and
make teeth half a tooth-space deep or long.

[Illustration: Fig. 8]

We now come to the consideration of the pallets and
how to delineate them. To this we shall add a
careful analysis of their action. Let us, before
proceeding further, “think a little” over
some of the factors involved. To aid in this
thinking or reasoning on the matter, let us draw the
heavy arc *l* extending from a little inside of
the circle *n* at *f* to the circle *n*
at *e*. If now we imagine our escape wheel
to be pressed forward in the direction of the arrow
*j*, the tooth *D* would press on the arc
*l* and be held. If, however, we should revolve
the arc *l* on the center *k* in the direction